Conclusion

A finite matter–geometry feedback step can be a genuine channel only after its classical controller, quantum instrument, geometric certificates, and observation boundary have been declared together.

The unconditional law uses subnormalized blocks and fixed completely positive transition maps. Exact observation compatibility is an adjoint inclusion. For stochastic histories, it must hold branchwise; the smallest future-sensitive observation spaces can be constructed backwards and, in the homogeneous finite case, stabilize after finitely many enlargements. Entangled spectators preserve every unnormalized history block after restriction when the entire controller is blind to them.

Implementation independence is conditional and testable: selective maps must agree on the declared continuation observables. Equal effects alone are insufficient. Informative classical records also cannot coexist with exact preservation, or exact recovery, of every quantum input.

The explicit qubit model proves that these requirements, an exact resource ledger, and quantitative stability can be satisfied simultaneously. Its geometric branches are strictly ordered slices of one fixed cone. That is a closed finite operational result, not a theory of semiclassical gravity.

The gravitational dynamics and field-theoretic source stages remain separate constructions.